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added THE AcmOM OF COAL D1 






. LDD8TS. By Ed. 

I d. Wtlllams, Jr., S H- 

I No. 14.— FRICTION OP AIH IS MINES. By J. J. AlWason. 
No. IB.-SKBW ABCHES. By Prof. B. W. Hyiie, C. B. 
No. 18.— A GRAPHIC METHOD FOR SOLVING CERTAIN 
ALGEBRAICAL E(iDATJONS. By Prof. Geo. L. 

I. 17.— WATBR AND WATER SUPPLY. By Prof. W. 

Corteld, M. A. 
>. IB. -SBWEiJlAaE AND SBWAGE UTILIZATION. : 

, " f •riiiilif ^ 

_^,>^o. W.~f ^r TRANBVEHSE 

ao.. ES. By Ji>lm B. 

ei- [. Bael, C. B. 



bNUlf 
U$ 






1^-" 



I- 




7 

TEE VAN NOSTBAHS SCIEBOE SEBIES. / 



No. 
No. 



No. 

No. 
No. 
No 
No. 

ro. 

No. 






22.— HIGH MASONRY DAMS. By John B. McMaster.y 

23.-THB FATIGUB OF MBTALS UNDKR BEPEATBO 
STRAINS, with yarious Tables of Results of Ex- 
periments. From the Qerman of Prof. Lndwlg 
Spangenberff. With a Preface by S. H. Shreye. 

84.-A PRACTICAL TREATISE ON THE TEETH OF 
WHEELS, with the Theory of the Use of Robin- 
. son's Odontograph. By Prof. 8. W. Robinson. 

26.— THEORY AND CALCULATIONS OF CONTINU- 
OUS BRIDGES, by Mansfield Merriman, C. E. 

28.-PBACTICAL TREATISE ON THE PROPERTIES 
OF CONTINUOUS BRIDGES. By Charles Bender. 

27.— ON BOILER INCRUSTATION AND CORROSION- 
By F. J.Rowan. 

28— ON TRANSMISSION OF POWER BY WIRE 
ROPES. By Albert W. Stahl. 

29. -INJECTORS ; THEIR THEORY AND USE. Trans- 
lated from the French of M. Leon Ponchet. 

ao— TERRESTRIAL MAGNETISM AND THE MAGNET- 
ISM OF IRON SHIPS. By Prof. Falrman 
Rogers. 

81.-THE SANITARY CONDITION OF DWELLING 
HOUSES IN TOWN AND COUNTRY. By George 
E. Waring. Jr. 

32— CABLE MAKING FOR SUSPENSION BRIDGES. 
' as exemplified In the construction of the East 
River Bridge. By Wilhelm Hildenbrand, C. E. 

83.— MECHANICS OF VENTILATION. By George W. 
Rafter, C. E. 

84.— FOUNDATIONS. By Prof Jules Gaudard, C. E. 
Translated from the French. 

85.— THE ANEROID BAROMETER: Its Construction 
and Use. Compiled by Prof. G. W. Plympton. 
8d Edition 

36.— MATTER AND MOTION By J. Clerk Maxwell 

87.— GEOGRAPHICAL SURVEYING: Its Uses, Methoas 
and Results. By Frank De Yeaux Carpenter. 

38.— MAXIMUM STRESSES IN FRAMED BRIDGES. 
By Prof. Wm. Cain. 

89.— A HANDBOOK OF THE ELECTRO-MAGNETIC 
TELEGRAPH. By A. B. Loring, a Practical Tel- 
egrapher. 2d Edition. 

40.— TRANSMISSION OF POWER BY COMPRESSED 
AIR. By Robert Zahner, M. E. 

41.-STRENQTH OF MATERIALS. By William Kent. 

42.— VOUSSOIR ARCHES, applied to Stone Bridges, Tun 
nels. Culverts and Domes. By Prof. Wm. Cain. 

No. 48.— WAVE AND VORTEX MOTION. By Dr. Thomas 
Craig, of Johns Hopkins University. 



No. 



No. 



o. 



No. 

No. 
No. 

No. 

No. 

No. 

'No. 
No. 



L 



y 






• /^/; f^rc 



.y 



WIRE ROPES. 



ALBERT W.' STAHL, M.E., 



arconb EttftUn, KebtseS. 



NEW YORK: 
D. VAN NOSTRAND COMPANY, 

St HuBRAT um 3T WtKUM STEKBT. 



» 



COFTRiaHT, 1880, 
BY 

D. Yam Nostrand Comphtt. 



.\ 



A 



V 



TvioJk '^' ^*^ 






/ 



2.3 



PREFACE. 



Since this little volume was first pub- 
lished, twelve years ago, the question of 
the economical transmission of power 
has become one of prime importance. 

Central stations have been established 
for the cheap production of power in 
large quantities, and the distribution of 
the same over considerable areas to 
thousands of consumers. The present 
tendency is toward still further centrali- 
zation of the production of power, and its 
transmission to any required points. 

While such extraordinary efforts are 
being made to cheapen the actual pro- 
duction of power, great care must be ex- 
s ercised that no unnecessary losses be sus- 
tained during its transmission. For 
many years, rapidly moving wire ropes 
•^ iU 



IV 



were undoubtedly the most efficient 
means of conveying power to great dis- 
tances; but the rapid strides which have 
been made in the development of elec- 
trical transmission have limited the field 
of the useful application of wire ropes. 
There are, however, certain limits between 
which the transmission _of power by wire 
ropes is yet more efficient than by any 
other methods ; and these limits we will 
attempt to define. 

The literature on this subject, espe- 
cially in the English language, is very lim- 
ited. Much of the practical part of the 
subject is well handled in the report of 
the U. S. Commissioners to the Paris Ex- 
position of 1867, and in pamphlets pub- 
lished by the J. A. Roebling^s Sons Co., 
the Trenton Iron Co. and several other 
firms engaged in the manufacture and 
installation of such plants. 

In Europe, where this method of trans- 
mitting power had its origin, its theory 
and practice have been investigated by 
Prof. P. Reuleaux, who has devoted a 
number of chapters to it in his various 
scientificworks, and by Prof. W. 0. Un- 



win, in his " Elements of Machine De- 
sign." It has also been extensively 
written on by Mr. D. H. Ziegler, of the 
firm of J. J. Rieter & Co., Switzerland, 
who have long been identified with such 
work. 

It is to the publications above men- 
tioned that much of the matter in the 
following pages is due. 



TRANSMISSION OF POWER 
BY WIRE ROPES. 



The fundamental problems of me- 
chanical engineering are those relating 
to the generation, transmission, and util- 
ization of power. But not all of these 
have hitherto received the same degree 
of attention ; and it is a well-known his- 
torical fact that economy in the genera- 
tion of power in the prime mover, and 
economy in its utilization in the ma- 
chine, have in most countries been far in 
advance of its economical transmission 
from the one to the other. 

Improvements in steam-engines and 
boilers, in hydraulic engines, water- 
wheels, and turbines, and in air, gas, and 
oil engines, have come in rapid succes- 
sion, until there seems but little room 
for further advance in this direction; 

7 



8 



and at the same time our machines and 
machine tools have been rapidly ap- 
proaching a state of comparative perfec- 
tion. But only in recent years has it 
been thought wox'th while to bestow 
much care and attention on the econom- 
ical transmission of the energy from the 
prime mover to the machine. 

Not many years ago this transmission 
of power was accomplished by means of 
cumbersome wooden shafts, upon which 
were wooden drums for the driving-belts; 
gearing also made of wood ; slow-moving, 
awkward contrivances for the purpose, 
and very wasteful of power. This stage 
is now happily passed, and the distribu- 
tion of power to short distances is ac- 
complished with but little waste, by rap- 
idly moving belts, and light steel shafting 
running in accurately fitted journals. 

In addition to the usual cases of short- 
distance transmission, there are two 
large classes of cases where the distance 
enters as a most important factor: the 
one comprises all those cases where the 
power of hitherto inaccessible sources of 
natural energy is to be transmitted to 



distant points, where it can be usefully 
employed; and the other comprises all 
those cases where the source of energy is 
itself accessible, but where it is desired 
to distribute the power to a number of 
independent small working centres. 

Although among the most efficient 
means of transmitting power to short 
distances, both belting, and shafting have 
the disadvantage that, when the distance 
becomes great, the intermediate mechan- 
ism absorbs an important portion of the 
power by vibrations, friction, and resist- 
ances of every nature; and for a dis- 
tance of several hundred feet we do not 
get, at one end of the transmission, more 
than an extremely small fraction of the 
power applied to the other.; thus, a shaft 
one mile long would transmit only about 
one half the energy imparted to it ; while 
a shaft two miles long, running in well 
made and lubricated bearings, would ab- 
fiorb the entire power in friction : in other 
Vords, no amount of power would suffice 
to turn it. 

In the case of a mere dead pull, as in 
working a pump, work is and has long 



10 



been transmitted to great distances ; as, 
by the long lines of ^^ draw-rods '' used 
in mining-regions to transmit the power 
of a water-wheel by means of a crank on 
its main axis, pulling, during half its 
revolution, against a heavy weight, and 
thus storing up energy for the return 
stroke, as the rods, on account of their 
flexibility, cannot be used to exert a 
pushing strain. Rotary motion, how- 
ever, cannot be economically produced 
in this manner. 

Of late years, much attention has been 
bestowed on the various means of trans- 
mitting power to distances; and each has 
been brought to a considerable degree of 
perfection. 

Four such methods are now in use, 
and have each their well-defined sphere 
of action. Thus we may transmit energy 
by means of electricity or wire ropes, or 
by hydraulic or pneumatic connection. 
As we shall see later, the great expense 
of the plant for the latter two methods, 
as well as their low efficiency due to fric- 
tion in the pipes, precludes their use ex- 
cept where special local circumstances 



J 



11 



render their other advantages of more 
importance than the question of econ- 
omy. The real competition, then, lies be- 
tween electricity and wire ropes ; and 
-where economy is the only feature to be 
considered, the point on either side of 
-which one or the other of these systems 
is preferable is fairly well defined. 

The undisputed credit of inventing 
the use of wire ropes for the transmis- 
sion of energy belongs to the Hirn 
Brothers, of Miilhausen, Switzerland.* 
To satisfy themselves on this point, the 
International Jury at the Paris Exposi- 
tion in 1867 made a thorough search 
through the registers of patents and 
other publications for many years, but 
failed to find anything bearing the least 
resemblance to this method. 

The principles underlying the trans- 
mission of power by wire ropes are : 

(1) The mechanical work done in any 
given time is equal to the resistance over- 
come, multiplied by the distance through 
which the resistance is overcome ; 

* See " Notice sur la transmission telodyna- 
mlque, par C. F. Hirn (Colmar, 1862)." 



12 



(2) In the performance of mechanical 
work, force may be exchanged for veloc- 
ity, or velocity for force. 

To illustrate, let us suppose a bar of 
iron, having a cross sectional area of one 
square inch, to move endlong at the rate 
of two feet per second. If the resist- 
ance overcome is, say, 5000 pounds, work 
will be performed at the rate of 10,000 
foot-pounds per second. Now, if we 
double the velocity of the bar, we will 
transmit twice the amount of work with 
the same strain, or the same work may 
be transmitted with only half the former 
strain. Supposing the proper intensity 
of tension in the bar to be 5000 pounds 
per square inch, we may thus, at this 
double velocity, transmit the same origi- 
nal amount of work by a bar having an 
area of only half a square inch. In a 
similar manner, if we move the bar with 
the velocity employed in wire-rope trans- 
mission, viz., about eighty feet per 
second, then, while doing the same 
amount of work, the strain on the bar will 
be reduced from 5000 to 125 pounds; 
and to maintain a tension of 5000 pounds 



13 



per square inch, the bar will only need a 
section of 0,025 square inch. To put an 
extreme illustration, we may conceive 
of a speed at which an iron wire as fine 
as a human hair would be able to trans^ 
mit the same amount of work as the 
original one-inch bar. 

By the application of these simple 
principles in Hirn's apparatus, energy is 
thus transmitted in the shape of consid- 
erable velocity and little force, while at 
the receiving-station it is again converted 
back into the generally more useful form 
of large force and little velocity. 



\ 



u 



MECHANICAL DETAILS. 

The construction of the apparatus is 
very simple. A tolerably large iron 
wheel, having a V-shaped groove in its 
rim, is connected with the motor, and 
driven with a perimetral velocity of usu- 
ally from 50 to 100 feet. 

Eound this wheel is passed a thin wire 
rope, which is led away to almost any 
reasonable distance (the limit being 
measurable by miles), where it passes 
over a similar wheel, and then returns 
as an endless band to the wheel whence 
it started. 

The peripheries of the driving-wheels 
may have an angular velocity as great as 
convenient ; the only limit, in fact, be- 
ing that the speed shall not be so great 
as to involve any danger of destroying 
the wheels by centrifugal force. The 
speeds which have been actually em- 
ployed in practice vary from 25 to 100 



15 



feet per second at the circumference of 
the pulley. 

The Wheels. — The wheels them- 
selves are made as light as is consistent 
with strength, not only for the sake of 
reducing the friction on the journals of 
their shafts to a minimum, but for the 
equally important object of diminishing 
the resistance of the air. It can hardly 
be doubted that abandoning spokes en- 
tirely, and making the pulley a plain 
disc, would considerably improve the 
performance, could such discs be made 
at once strong enough to fulfil the re- 
quired functions, and light enough not 
materially to increase the friction. 

The wheels are usually made of cast- 
iron or steel, and, beside their lightness, 
have but one peculiarity of construction, 
and that is a highly important one : at 
the bottom of the V-shaped groove, go- 
ing around the circumference, a little 
trough is formed, in which the filling is 
placed, as shown in Pigs. 1 and la. 

The materials used for this filling are 
many in number, and will be discussed 



16 
n»i. 



17 



further on. The rope should always run 
on a filling of some kind, and not direct- 
ly on the iron, which would quickly wear 
it out. 

Fig. I a. 




For wheels of over 14 feet diameter, 
the wrought-iron construction shown in 
Fig. lb is probably the best, combining 
lightness and strength; but wheels of 
such large size are not usually found 
necessary. 



18 
Fig. I b. 



10 



The rope i^ not tightly stretched over 
the wheels^ hut^ to all appearances^ hangs 
loosely on the same. But the rope does 
not slip^ as the tension caused by its own 
weight presses it hard against the rims 
of the wheels if the latter are of proper 
size. The body of the driving-wheel 
(Fig. la) differs very little from that of 
a belt-pulley; and it can always be pro- 
portioned as a belt-pulley, having to 
transmit the same power with the same 
velocity. 

The sides of the rim are usually made 
to slope about 25° to 30° from the verti- 
cal (Fig. 1). This slope, if used in a 
double wheel, such as are used at inter- 
mediate stations, would give an extreme- 
ly heavy central rib, on which account 
the sides of the latter are usually made 
steeper, viz., about 15° from the verti- 
cal. 

Even when the greatest care is taken 
in the installation and maintenance of a 
transmission, it seems impossible to pre- 
vent more or less oscillation and swing- 
ing of the ropes against the sides of the 
wheel-rims, resulting in rapid wear of the 



20 



ropes. This evU may be to a great ex- 
tent remedied by making the section of 
the wheel rim more as shown in Fig. Ic, 
flaring out the sides at angles of 45° with 
the vertical. This would be specially 
beneficial where the ropes are exposed to 

Fig. I c. 




a high side wind, but is attended with 
several disadvantages, particularly in the 
case of double-grooved wheels (compare 
Pigs. Id and le). The difficulty and ex- 
pense of making the wheels would be 
greater, and the increased distance be- 
tween the ropes would result in consider- 
able side pressure on the bearings of the 
shafts. 
Wheels from about nine feet in diame- 



31 
FIf. Id. 




22 



ter up are usually cast in halves and 
afterward fastened together on the shaft. 
In order that the centrifugal force may 
not become dangerous, the perimetral 
velocity should not exceed 90 to 100 feet 
per second. Velocities up to 90 feet 
have been frequently used without any 
prejudicial results whatever. Owing to 
the high speed employed, it is abso- 
lutely essential that the wheels should be 
perfectly balanced. 

The filling first employed by Mr. 
A. Him consisted of a strong leather belt 
covering the rim and fastened to the 
same by nails and wooden wedges, as 
shown in Figs. 2 and 3. 

With wheels of large diameter, he was 
obliged to make this belt of several 
pieces, thereby weakening it consider- 
ably. This style of filling, however, 
rarely lasted longer than a few months. 
Hirn was then induced to try rubber ; but 
with very large wheels, the rubber was 
found to be unsuitable on account of its 
great expansion when heated, so that 
when wheels filled with it were exposed 
to the direct and strong rays of the sun. 



S3 

the rubber became soft and was cat by 

the rope, or it expanded over the edge of 

the wheel, cauBing the rope to be thrown 

Fig. 1. 




oft. In some cases, where the filling ex- 
panded greatly at noon, it retamed to 
its original position during the night. 
On the other hand, there are aaees 



24 



known when in cold nights, during the 
stoppage of the transmission, the rope 
would freeze to the rubher filling. On 
starting in the morning, large fragments 
of the brittle rubber were torn out. Be- 
sides this, the rubber was also slowly dis- 
solved by the oil and grease on the rope. 
After some unsuccessful attempts at 
filling with hippopotamus-skin, willow 
and poplar wood were tried, giving 
quite passable results. Strips of poplar 
wood about f inch thick and 7 to 10 feet 
long were planed to the proper section, 
softened in hot water, and then driven 
in without any special fastening. This 
process was very simple, allowing the 
wheels to be refilled quickly and at 
slight expense. The main difficulty was 
that the filling sometimes became loose, 
owing to the drying and shrinking of 
the wood during the hot season. This 
was partly prevented by driving pieces 
of wire through the filling and the rim 
of the wheel. The wood was also soft- 
ened in hot glycerine instead of hot water, 
thus rendering it less subject to the vary- 
ing hygrometric condition of the air. In 



35 



spite of these precautions, a wooden fill- 
ing rarely lasted more than six or nine 
months when the wood was most care- 
fully selected, while, if knots or unsound 
spots were present in the filling, it wore 
out in a still shorter period. Various 
other woods were then tried, but willow 
and poplar were found to bo the most 
durable as well as the cheapest. 

As wood wears less when subjected to 
strain and pressure across the direction of 
the grain, this method was also tried, 
notably at the Schaff hausen Water- works. 
In this case, small pieces were cut, having 
the fibre running from side to side of the 
rim of the wheel. These pieces were then 
dried thoroughly, and frequently im- 
mersed in linseed varnish until they were 
completely saturated with the latter, thus 
becoming more durable and air-tight. 
Notwithstanding these precautions, some 
of the pieces became loose, and, although 
more durable than the plain wood filling 
previously described, they did not last 
longer than about one year. A further 
trial was made with wood filling in which 
the fibres ran radially, but with no better 



26 



results. But this last method has the 
advantage that, when the rope wears a 
groove into the wood, the sides do not 
split off as easily as in the two other 
styles. 

Cork has also been tried to some ex- 
tent, but it has proved of little value for 
transmitting any considerable force, as it 
wears out very rapidly. 

Again, by wedging the groove full of 
tarred pakum, a cheap filling was obtained, 
nearly as good as leather, and not so 
tedious to insert. 

Another plan was to revolve the wheel 
slowly, and let a lot of small-sized tarred 
ratlin or jute yarns wind up on themselves 
in the groove. After a day or two of 
running, the pressure of the rope, to- 
gether with the tar, made the filling com- 
pact. 

The first attempts with radial leather 
filling were made about 1865 ; and it was. 
soon found that this method of filling 
was so decidedly superior to all others 
that it has now come into almost exclu- 
sive use. It is easily inserted by any or- 
dinary mechanic. The separate pieces of 



27 



leather are driven hard against each other 
in the groove of the wheel, which has 
been carefully turned true. The key or 
closing piece is made of india-rubber, 
which is first softened in hot water and 
then driven into its proper place. The 
greatest wear of the filling occurs not, as 
might be expected, in the driving-wheels, 
but in the intermediate carrying- sheaves, 
and there principally in the smaller 
wheels. 

The life of leather filling depends on 
the quality of leather used, and on the 
radial thickness of the pieces. It is also 
affected by the tension, and general con- 
dition of the ropes. It may usually be 
estimated at about three years. 

Latelv a new kind of hard rubber fill- 
inghas come into extensive use, and seems 
to be meeting with considerable success. 
The shape of the filling is shown in the 
full-size sketches on page 28. 

A convenient method of lining the 
inside faces of the flanges of trans- 
mission wheels is illustrated in Fig. 4. 
Segments of sole-leather, B, are secured 



28 




to tho flange. A, by rivets, and thus the 
rope, ia applications where it^ is exposed 
to side winds inducing lateral swiijlng, is 



protected from wear npon the sides of 
the rim. 

The following table gives the usual 
weights and prices of transmission wheels 
(Figs. 1 and la) with hub bored to re- 
quired size, and furnished with either 
rubber or leather filling : 



30 



TRANSMISSION WHEELS. 



DiamfUr in Feet. 


W«i«:htiQpoun(Ui. 


Price per WhaeL 


u 




• « • r 


» 7 


2 




• * * • 


8 


3 




• • • • 


20 


4 




400 


28 


5 




685 


40 


6 




950 


65 


7 




1100 


80 


8 




1400 


110 


9 


) ca.st in 
] halves 


1680 


190 


10 


2300 


210 



The price of wheels such as shown in 
Fig. lb would be : 14 ft. diameter, about 
$350 ; 16 ft. diameter, about $400. 

There is usually a trade discount, from 
above prices, of from 5 to 10 per cent. 

Additional rubber or leather filling is 
sold at about 60 cents per pound. 

The Hopes. — The driving-rope usually 
employed in this country consists of six 
strands, with seven iron or steel wires to 
each strand (Fig. 5). The strands are 
spun around a hempen centre or core, 
thus obtaining the necessary flexibility. 



i 



If rf = diameter of wire in inches ; 
D = diameter of rope in inches ; 
w = weight of rope in pounds per 
running foot, — 
then for this kind of rope 
7> = 9 (/; . 
w = 1.5 Z>' (very nearly). 

The following table gives further partic- 
ulars concern ing the above rope, represent- 
ing the practice of the principal Ameripan 



32 



firms engaged in the business of making 
such installations : 

WIRE ROPE 

CONSISTING OF 6 STRANDS OF 7 WIRES EACH. 

IRON. 



Trade 
No. 



11 
12 
18 
14 
15 
16 
17 
18 
19 
20 
21 
22 
28 
24 
25 



Diam- 


Price 


eter in 


per 


inches. 


foot. 


,^ 


$0.48 


lu 


.89 


Ih 


.34 
.27 


1 


.23 


z^ 


.19 


yi 


.14 
.12 

.10* 


A 


.08 


7^ 


.07 


i" 


.05* 


7^ 


.05 


■^ 


.04 


b\ 


.03* 



Estimated 
Weight per 
' foot, in 
pounds. 



8.87 
2.77 
2.28 
82 
50 
12 
88 
70 
57 
41 
81 
23 
0.19 
0.16 
0.125 



Breaking 

Stress, in 

tons of 2000 

lbs. 



86.0 
80.0 
25.0 
20.0 
16.0 
12.8 
8.8 
7.6 
5.8 
4.1 
2.88 
2.18 
1.65 
1.38 
1.08 



Proper 
Working 
Load in 

tons of 
2000 lbs. 



9 



^ 



2 

1 



SPECIAL CAST-STEEL. 



11 


jw 


$0.70 


8.87 


88.88 


22.0 


12 


1&4 


.60 


2.77 


67.20 


16.8 


18 


ii 


.50 


2.28 


60.67 


15.2 


14 


.40 


1.82 


89.84 


10.0 


16 


1 


.82 


1.50 


81.82 


8.0 


16 


i 


.25 


1.12 


24.70 


6.2 


17 


.19 


0.88 


18.48 


4.6 


18 


.16 


O.TO 


16.32 


4.0 


19 


.14 


0.57 


12 44 


8.1 


20 


JL 


.11 


0.41 


9.88 


2.8 


tl 


79 


.68 


0.31 


6.89 


1.7 


22 


Ju 


.071 


0.28 


5.28 


1.8 


88 


fZ 


.or 


0.19 


8.98 


1.0 


24 


'] V 


.05 


0.16 


8.25 


.81 


26 


* 


.04* 


0.125 


2.96 


.76 



34 



For cases where unusual conditions 
compel the use of specially small wheels, 
it is better to employ one of the more 
flexible ropes shown in Figs. 5a and 55, 
for which the formulas subsequently to be 
given can be readily modified. 

The following table gives particulars 
concerning the rope shown in Fig. 6b. 

WIRE ROPE 

CONSIST IN6 OF 6 STBANDS OF 19 WIRES EACH. 

IRON. 



Trade 
No. 



Diam- 
eter, in 
inches. 



Price 

per 

foot. 



$1.00 
.78 
.69 
.68 
.53 
.43 
M 
.29 
.26 
.20 
.16 
.14 
.12 
.10 
.08 



Estimated 

Weight per 

foot, in 

pounds. 



7.75 
6.11 
5.09 
4.00 

2.90 
2.42 
1.95 
1.53 
1.16 
0.85 
0.60 
0.47 
0.37 
0.26 



Breaking 

Stress, in 

tons of 2000 

lbs. 



74.00 

65.00 

54.00 

44 00 

39.00 

83.00 

27.00 

20.00 

16.00 

11.50 

8.64 

5.13 

4.27 

3.48 

2.50 



Proper 
Working 
Load, in 

tons of 
2000 lbs. 



SPECIAL CAST-STEKI.. 



The special Cast-Steel Rope is made 
from wire manuEactured for the purpose, 
of high tensile strength (about 175,000 
pounds per square inch of section), and 
at the same time of exceptional tough- 
ness and ductilitj. 

There is usually a trade discount, from 
prices given in above tables, of 25^ to 
35^ on iron ropes and about 45^ on steel 
ropes. 

In splicing a wire rope, the greatest 
care must be taken to leave no project- 
ing ends or thick parte in the rope. On 
this subject; I can do no better than give 
Messrs. Eoebliug's directions for making 



36 



a long splice in an endless running rope 
of half -inch diameter:* 

" Tools required : One pair of nippers, 
for cutting off ends of strands ; a pair of 
pliers, to pull through and straighten 
ends of strands; a point, to open strands; 
a knife, for cutting the core ; and two 
rope-nippers, with sticks to untwist the 
rope ; also a wooden mallet. 

" First. — Heave the two ends taut with 
block and fall, until they overlap each 
other about twenty feet. Next, open 
the strands of both ends of the rope for 
a distance of ten feet each ; cut off both 
hemp cores as closely as possible (Fig. 6), 
and then bring the open bunches of 
strands face to face, so that the opposite 
strands interlock regularly with each 
other. 

" Second, — ^Unlay any strand, «, and 
follow up with the strand 1 of the other 
end, laying it tightly into the open 
groove left upon unwinding a, and mak- 
ing the twist of the strand agree ex- 

*Sefe "Transmission of Power by Wire 
Ropes," by W. A. Roebling, C.E. 



38 



actly with the lay of the open grooTO, 
until all but about six inches of 1 are 
laid in, and a has become twenty feet 
longo Next cut off a within six inches 
of the rope (Fig. 7), leaving two short 
ends, which must be tied temporarily. 

" Third, — Unlay a strand, 4,of the op- 
posite end, and follow up with the strand 
/*, laying it into the open groove, as be* 
fore, and treating it precisely as in the 
first case (Fig. 8). Next, pursue the 
same course with h and 2, stopping, how- 
ever, within four feet of the first set; 
next with e and 5 ; also with c, 3 and dy 
4. We now have the strands all laid into 
each other's places, with the respective 
enes passing each other at points four 
feet apart, as shown, in Fig. 9. 

*' Fourth, — These ends must now be se- 
cured and disposed of, without increas- 
ing the diameter of the rope, in the fol- 
lowing manner : Nipper two rope-slinga 
around the wire rope, say six inches on 
each side of the crossing-point of two 
strands. Insert a stick through the loop 
and twist them in opposite directions, 
thus opening the lay of the rope (Fig. 



39 



10). Now cut out the core for six inches 
on the left and stick the end of 1 under 
a, into the place occupied by the core. 
Next, cut out the core in the same way 
on the right, and stick the end of a in 
the place of the core. The ends of the 
strands must be straightened before they 
are stuck in. 

Now loosen the rope-nippers and let 
the wire rope close. Any slight inequal- 
ity can be taken out by pounding the 
rope with a wooden mallet. 

" Next, shift the rope-nippers, and re- 
peat the operations at the other five 
places. 

" After the rope has run for a day, the 
locality of the splice can be no longer 
detected. There are no ends turned un- 
der or sticking out, as in ordinary splices, 
and the rope is not increased in size nor 
appreciably weakened in strength." 

I have dwelt so minutely on the pro- 
cess of splicing, because practical expe- 
rience has demonstrated that a man who 
can splice a wire rope well is something 
of a rarity. Some of the best ship-rig- 
gers are utterly nonplussed when a wire 



40 



rope is presented to them to be spliced; 
and the splice they produce is usually 
half again as thick as the rope^ and ut- 
terly useless for the intended purpose. 

Wire ropes with wire centers are 
sometimes employed for the transmission 
of power, but they have not usually 
proved satisfactory in practice, wearing 
out much more rapidly than ropes with 
hemp centers. The only advantage to 
be gained by the use of wire rather than 
hemp centers is in the increased strength 
of the ropes, enabling a certain amount 
of power to be transmitted with a smaller 
rope, and in the fact that such ropes 
stretch less than those with hemp cen- 
ters. 

This latter difficulty can be almost en- 
tirely obviated, as will be explained fur- 
ther on; and as the ropes with hemp 
centers are much more durable, they are 
now used almost exclusively. Another 
disadvantage found in the use of ropes 
with wire centers is that the splice must 
be made nearly twice as long as when 
hemp is used for the center. This must 
be done to prevent the two ends of the 



41 



rope from slipping out, as the coefficient 
of friction is not so great between iron, 
and iron as between iron and hemp. 

As, in splicing, the wire center is cut 
off at the splice and not spliced in, it .ia 
iree to move in the rope in the direction 
(Of least resistance. It consequently hap- 
pens that the wire center frequently pro- 
trudes through the strands of the rope* 
This may be partly remedied by sewing 
with cord through the center and the 
outside wires, thus fastening them in 
their proper relative positions. In a 
short time, however, the center will 
again project; we are then compelled to 
cut off the projecting end, and repeat 
the operation of sewing with cord, which 
does not by any means improve the du- 
rability of the rope. The princi pal diffi- 
culty — the excessive wear of the outer 
wires — is common to both kinds of ropes* 
This wear is caused chiefly by the friction 
of the wire on the sides of the wheel- 
groove when the rope for any reason 
runs unsteadily and swings against the 
sides of the groove. The ropes get flat 
in places and finally the wires break. 



42 



It is difficult to lay down any general 
rule as to the duration of the ropes, for 
this depends on the conditions under 
which they work. In ordinary practice, 
about one year can be safely counted on ; 
and although the ropes will usually last 
considerably longer, it is customary to 
replace them before they finally give out, 
to avoid interruption in the work. If 
duplicate ropes are kept on hand ready, 
and spliced to the proper length, and if 
a short interruption of the transmission 
is not of much moment, the ropes may 
be run until they are actually worn out, 
and will in such cases probably average 
a life of nearly two years. 

To prevent the wear of the wires, and 
thus to make the ropes more durable, 
has been the object of several inventions ; 
all of which were attempts at surround- 
ing the wires with a flexible and durable 
covering, protecting the wires, and at 
the same time not increasing the difficul- 
ties of splicing. It was also thought 
that, if this could be made a practical 
success, the filling in the wheels might 
be entirely dispensed with. Instead of 



43 



the rope running on the soft filling of 
the wheel, the soft envelope of the rope 
might run directly on the cast-iron rim. 
Nearly all the experiments in this direc- 
tion have failed, and it is only recently 
that the firm of Martin Stein & Co., 
Miilhausen, Switzerland, have partially 
solved this problem. They have for some 
time been making ropes in which coarse 
cof'on yarn was spun about the separate 
wires, the latter being then spun into 
rope. In this way they obtain a soft 
body between the separate wires, and also 
a soft envelope for the whole rope, which, 
when saturated with a special resinous 
compound, is said to be very durable^ 
The rope also seems less affected by varia-^ 
tion of weather, being partly protected 
against sun and rain by the covering. 
For the same reason, rusting is not so 
likely to occur. If, in connection with 
these covered ropes, wheels with leather 
filling were employed, the adhesive force 
on the pulleys would become much greater 
than with the ordinarv ropes, thus reduc- 
ing the necessary tension in the ropes. 
These ropes have not come into use in 



44 



this country; and only experience will 
determine whether their durability is 
sufficient to warrant their more general 
introduction. 

The price of such covered wire ropes 
is naturally greater than that of ordinary 
wire ropes ; but if, as the manufacturers 
claim, they may be expected to last about 
three times as long as ordinary wire ropes, 
it would evidently be true economy to use 
the more expensive rope. 

In handling wire rope, it must not be 
coiled and uncoiled like hemp rope. 
When it is received from the manufac- 
turers, wound on a reel, the latter should 
revolve on a spindle while the rope is paid 
off ; when in a coil not on a reel, the coil 
should be rolled on the ground like a 
wheel, the rope being thus paid off so as 
to avoid any danger of untwisting or 
kinking. 

It is also a cardinal point to make the 
driving-wheels as large as possible, as will 
appear later in considering the stresses on 
the rope. 

Under no circumstances should galvan- 
ized rope be used for running-rope, as 



45 



the coating quickly wears ofE, and rusting 
then proceeds with great rapidity. To 
preserve the rope, raw linseed oil or a 
mixture of the same with Spanish brown 
or lamp-black is to be preferred. A heated 
mixture of grease and resin is sometimes 
used with success, as are also many of the 
heavier lubricating compounds. 

Supports for the Wheels. — The driving- 
wheels and their shafts are supported at 
the necessary height on strong wooden or 
masonry foundations, braced, if neces- 
sary, to resist the horizontal pull of the 
ropes. The length of the shaft between 
journals should not be less than the 
radius of the wheel. The onlv im- 
portant feature about mounting the 
wheels is to get them absolutely vertical 
and to get all the wheels carrying the 
same rope in the same vertical plane. 
The efficiency and durability of the sys- 
tem will be much impaired by neglect of 
these points. 

The supports themselves range in style 
and dimensions from the simple wooden 
frame shown in Fig. 11 and the iron one 



46 



of Fig. 12 to the more ornamental stone 
structure of Figs. 13 and 14, and thence 
to such large masses of masonry as are 
shown in Plates I and II. 

Fig. II. 




Carrying Sheaves, Intermediate Sta- 
tions, etc. — When the distance of trans- 
mission materially exceeds three or four 
hundred feet, or when there is not suf- 
ficient height available for the sag of the 
rope, the latter is usually supported at 
intermediate points by carrying-sheaves. 






47 



Sometimes it is sufficient to support only 
the following side of the rope, and gener- 
ally, whatever the number of sheaves, the 

Fig. 12. 




driving side is supported at one less po*flt 
than the following side. The same num- 
ber of sheaves may, however, be used. 



60 



placing one over the other. The sheaves 
must never be placed side by side, as has 
been sometimes done to the great detri- 
ment of the transmission, the rope wear- 
ing out very rapidly against the side of 
the wheel-rim. 

The sheaves supporting the driving 
side of the rope must in all cases be of 
equal diameter with the driving-wheels; 
and this for the same reason that the lat- 
ter are usually made of so large a diam- 
eter. For whether the rope laps half way 
round on the driving-wheels, or only quar- 
ter way round on the carrying-sheaves, 
makes no difference — the tension due to 
bending is the same in both cases. With 
the following side, however, a somewhat 
smaller wheel may be used, owing to the 
fact that there is less direct tension on 
this side, and it is therefore better able 
to stand the additional tension due to 
bending. 

The system of carrying-sheaves may 
generally be replaced with advantage by 
that of intermediate stations. When the 
latter is used, we have at each station, in- 
stead of two carrying-sheaves, one double- 




egarde. 



SCS& 



51 



grooved wheel (see Fig. 14). The rope, 
instead of running the whole length of 
the transmission, runs only from one sta- 
tion to the other. It is advisable to make 
the stations equidistant, so that a rope 
may be kept on hand, ready spliced, to 
put on the w&eels of any span should its 
rope give out. 

For very powerful transmissions, it be- 
comes advisable to employ two parallel 
ropes, either of which should be capable 
of transmitting the entire power. Even 
if the latter condition is not adhered to, 
it yet often happens that two parallel 
ropes are employed. In all such cases it 
is almost impossible to preserve equality 
between the tensions of the parallel ropes 
and between the diameters of their wheels. 
The best arrangement seems to be to have 
the two 6?rVviw^-wheels rigidly connected 
to the same shaft, but to let the twofold 
lowing-wheels run loose on their shafts, 
connecting them by a differential gear, 
such as shown in Fig. 15. 

The rope-wheels are rigidly connected 
with the bevel wheels, B and D respec- 
tively, the latter being in gear with the 



53 

bevel wheels A and C. The axes of A 
and C are in the same straight line, and 
they are supported in a rigid frame firm- 
ly connected to the main shaft. The 
resolt is that, when the teosiouB of the 
Fif. 15. 



topes are not the same, there is a slight 
additional rotation of one wheel or the 
other, causing the equalization of the 
tension. This produces slight vertical 
oscillations, which have, however, no 
prejudicial influence on the working of 
the ropes. 



■s^^ 



53 



In case one of the ropes should break, 
the power transmitted on the other would 
no longer rotate the shaft, but would 
cause the violent rotation of the freed 
wheel. A brake is usually so connected 
with the apparatus as to stop the prime 
mover in such an event. To avoid any 
danger to the freed wheel from excessive 
speed of rotation, it has been proposed to 
form the gears A and C as sectors only, 
as shown to right of figure, in which case 
the freed wheel would be promptly 
thrown out of gear. 

If it is required to change the direc- 
tion of the rope at any point, it can be 
done by the interpolation of horizontal 
sheaves of same size as driving-wheels 
(Fig. 16). 

This method is not, however, to be 
recommended. It will usually be found 
much better to end the driving-rope 
over an ordinary vertical driving-wheel 
(a. Fig. 17), the shaft of which is con- 
nected by bevel gears with the shafts of 
similar wheels leading off new ropes at 
the desired angles. This arrangement is 
also usually adopted for a distributing 



54 

Fif.lt. 




55 



station^ where the power brought thus 
far by a single rope or a pair of parallel 

Fig. 17. 




Bevei Gear 

ropes is to be distributed to consumers 
in different directions. 



56 



Maintenance.* — In the transmission 
of power by wire ropes, the greatest at- 
tention must be paid to keeping the 
ropes and the lining of wheels in thor- 
ough* repair. Even when they are ex- 
ceedingly taut on the wheel at first, it 
has been found by experience that, after 
a short time, the ropes stretch consider- 
ably. This causes them, particularly in 
summer, to sag so much as to incapaci- 
tate them from transmitting the whole 
force, causing them to slip on the 
wheels ; or they begin to drag on the 
ground or other obstructions. This 
evil may be partially remedied by short- 
ening and again splicing the rope, which, 
however, should be avoided as long as 
possible, as the rope is injured more 
by several resplicings than by long run- 
ning under the regular working ten- 
sion. It is of course evident that a wire 
rope will stretch more as the wires make 
a greater angle with the axis of the rope; 
but as a rope having its wires parallel to 
the axis would be useless, we must keep 

, . — - - 

* See Ziegler's '*Betrieb und Insiandhal- 
tung der Drahtseiltriebe " (Wlnterthtlr, 1871). 



57 



the angle at its minimum value^ as dic- 
tated by practical experience. 

Experiments made with a view to 
stretching the ropes before putting them 
into use have not been very successful. 
It is only lately that the problem has 
been partially solved by Mr. D. H. Zieg- 
ler^s method of compressing the ropes 
while subjecting them at the same time 
to a great tensile strain. Wire ropes 
with wire centers, as sold in the market, 
are stretched in this manner from .22 to 
1.2 per cent. 

Wire ropes with hemp centers, as gen- 
erally employed for the transmission of 
power, are stretched from .71 to 2.6 
per cent, of their original length, with- 
out at all impairing their strength. 

Although this is a great step in ad- 
vance, reducing the stretching of the 
rope in use, with its accompanying dis- 
turbances, to a minimum, yet even this 
is not sufficient to maintain a constant 
tension and deflection in the rope, and 
we are often compelled to use other 
means to restore to the same its original 
tension. 



58 



The simplest and most effective way 
of attaining this end is by refilling the 
rims of the wheels, i.e., by increasing 
their respective diameters to the proper 
amount, which is done in the following 
manner. Fig. 18 shows the cross-sec- 
tion of a wheel with leather filling, and 
Figs. 20 and 21 the same wheel with its 
diameter enlarged by the superposition 
of the new filling, which is best made of 
poplar or willow wood. It is made by 
taking straight pieces of about IJ inches 
in thickness, planing them into the nec- 
essary shape to fit the rim of the wheel, 
or merely cutting them into that shape 
by means of a circular saw, and provid- 
ing their upper surfaces with grooves for 
the ropes. These pieces (Fig. 19) are 
made from four to six feet in length, 
and are provided on their insides with 
saw-cuts going half way through the 
wood. The pieces are first steeped in 
water for a day or two, to render them 
more flexible. They are then nailed to 
the leather filling by means of suitable 
wrought nails, which should be some- 
what longer than the thickness of both 



fillings together, so that after paeaing 
through the leather they may strike the 
iron below and be clinched, thus afford- 
ing a better hold. The nails must be 
driven aa shown, and especial care must 



rta. II. 



be taken that there are no projecting 
ends within reaeh of the rope. The 
whole operation can easily be performed 
in an hoiir, without throwing oflf the 
rope. In case the filling of one wheel in 
this manner is not sufficient to accom- 



61 



plish the desired result, the same opera- 
tion is performed on the other wheel. If 
this is still insufficient, the whole process 
is repeated with a second layer. When 
the rope has finally become of a constant 
length, which usually takes place in the 
course of a few months, we may care- 
fully remove all but the leather filling, 
and then shorten the rope to the proper 
length, allowing it to run on the original 
filling. After this treatment, there is 
usually no more trouble to be appre- 
hended from this source. 

When the transmission is in good run- 
ning order, the ropes should run very 
steadily and without swaying laterally. 

To ensure such results, a few princi- 
pal points are to be specially looked after. 
In the first place, it is absolutely neces- 
sary to balance the wheels perfectly ; as, if 
they are not perfectly circular and well 
balanced, the centrifugal force, at the 
velocity with which they are driven, ex- 
ercises a very prejudicial effect on the 
bearings of the shaft, as well as on the 
rope. The bearings wear out faster and 
more power is wasted in useless friction. 



62 



while the rope begins to swings sometimes 
to such an extent as to be thrown vio- 
lently against the side of the wheel- 
groove, thus wearing out very rapidly. 

In mounting a transmission, the 
greatest care should be taken to get the 
wheels in the same vertical plane and 
the shafts perfectly horizontal, inas- 
much as any deviation from this position 
immediately shows itself in the swaying 
of the rope, and, in addition, the latter 
rapidly wears out through friction on 
the wheel-rims. 

In case the filling is in bad condition 
and worn unequally, it causes the rope 
to swing in a vertical plane. The remedy 
is to cut the filling so as to make it 
equally thick all around, or, in case the 
rope is also too slack, the filling may be 
increased in thickness, as already ex- 
plained. 

If there are ends of wires projecting 
from the rope, then every time that one 
of these projections passes over the 
wheel, the rope receives a slight shock, 
causing it to swing. The same action 



63 



takes place if torn or loose strands occur 
in the rope. 

If the rope has been badly spliced or 
given a false turn or kink, it will not 
run steadily. 

When the rope has stretched to such 
an extent as to touch the ground or 
other obstructions, it begins to swing 
yiolently. An attempt has sometimes 
been made to remedy this by putting in 
a little roller or guide, which, however, 
usually makes matters worse". 

There are some other causes which 
induce an irregular action in the rope. 
For instance, if a wire rope is trans- 
mitting a constant power to a certain 
distance, and if the wheels, ropes, etc., 
are in good order, it will run steadily as 
long as the power transmitted corre- 
sponds to a certain tension and deflection 
in the rope. But now, if some of the 
machines are suddenly thrown in or out 
of gear, the tension in the rope and 
its corresponding deflection will be 
changed, thus causing the motor to adapt 
its speed to suit the altered demand for 
power, the rope at the same time sway- 



64 



ing gently in a vertical plane. This 
property is of great value, particularly 
in long transmissions, as it prevents 
sudden changes in velocity, the rope it- 
self acting as a sort of governor. 

Wire ropes are sometimes employed to 
transmit the power of a steam-engine to 
a distant building, or to combine its 
power with that of some hydraulic mo- 
tor. In such cases, we must be careful 
to insure the regular action of the 
steam-engine ; as it often happens, par- 
ticularly in the case of an expanding, 
single-cylinder engine, with a light or 
badly balanced fly-wheel, that the speed 
during a stroke is very irregular. If we 
attempt to transmit the power of such 
an engine by means of wire ropes, the 
result will be a series of oscillations in 
the latter, in synchronism with the 
stroke of the engine. When this oc- 
curs, it can only be remedied by using a 
heavier and better balanced fly-wheel, 
or by adding a second cylinder to the 
engine. When a rope is used in con- 
nection with a steam-engine, the latter 
should be provided with a very powerful. 



66 



quick-acting governor, in order to pre- 
vent the overrunning of the engine if 
the rope should suddenly break. Such 
an accident happened some years ago in 
a cotton-spinning establishment in Al- 
sace, causing the complete destruction of 
a large steam-engine. 



Fig. 22. 




To facilitate the putting on of pre- 
viously spliced ropes, the wheels are 
often overhung instead of having their 
shafts supported at both ends. lii such 
cases, the application of the ropes to the 



66 



wheels is much facilitated by the simple 
device shown in Pig. 22. It consists sim- 
ply of a few feet of angle iron, bent to a 
curve of about half or two thirds the 
diameter of the wheel, and having one 

Fig. 23. 




end lying in the groove of the wheels and 
held there by a couple of bolts. The 
wheel being in position shown in Pig. 23, 
the rope can easily be laid in the groove 
of the angle-iron leader ; and giving the 
wheel half a revolution in the direction 



67 



of the arrow, brings the] rope entirely 
into the wheel groove (Fig. 24). The 
angle iron leader is then taken off and 
the transmission is ready to go ahead. 

Fig. 24. 




In case the driving-rope crosses streets 
or other thoroughfares, it is essential to 
prevent obstruction to the latter or dan- 
ger to passing persons or vehicles in case 
the rope should break. The simplest 



68 



means of accomplishing this result con- 
sists in stretching two fixed wire ropes 
across the thoroughfare, approximately 
parallel to and about one foot above 
and three or four feet on either side of 
the lowest position of the lower side of 
the transmission rope. These two fixed 
ropes are connected at every 9 or 10 feet 
by light round iron rods, curved down 
in the center to two or three feet below 
the line of the driving-rope. A sort of 
continuous net is thus formed, effectu- 
ally preventing the loose ends from drag- 
ging on the ground in case of fracture. 
In such cases, any gradual stretching of 
the driving-rope must be remedied at 
intervals sufficiently frequent to prevent 
it from touching the cross-rods. 



69 



STRESSES m THE ROPE. 

Th£ principal stresses in a wire rope in 
motion are — 

(1) Direct.tension corresponding to the 
power transmitted, and due to the weight 
of the rope itself, and to the necessary 
stretching of the rope over the wheels to 
insure sufficient friction; 

(2) Tension and compression in the por- 
tion of the rope at any time in contact 
with circamference of wheel, due to the 
bending of the wires; 

(3) Tension due to the centrifugal ten- 
dency of the portion of the rope at any 
time in^ contact with circumference of 
wheel. 

Direct Tension. — Taking up the con- 
sideration of the first of these stresses, 
let Fig. 25 represent a wheel about a por- 
tion of whose circumference is wrapped 
a perfectly flexible rope, the arc of con- 
tact being ft The wheel and the rope 



70 



are supposed to tend to move in the di- 
rections of the inner and outer arrows 

Fig. 25. 




respectiyely, their motion being just 
barely prevented by their total mutual 
friction jPdue to the tension of the rope. 



?1 



This friction for any length of arc is 
equal to the difference of tension at the 
two ends of the arc, and is also equal to 
the coefficient of friction between the 
rope and the wheel, multiplied by the 
normal pressure over that arc. Let / rep- 
resent this coefficient of friction, let T 
represent the varying tension of the rope 
along the arc of contact with the wheel, 
and let T^ and T^ represent the tensions 
of the driving and following portions of 
the rope respectively. 

Then for any elementary arc d 6, the 
normal pressure over which is T d 6, the 
friction will be 

dF=zdT=fTde. 

Integrating this expression over the 
whole arc of contact, 6, we get 

T T 

Nap. log. ^i =/^, and -^ =«/«, 

{e being the base of the Naperian system 
of logarithms) ; so that the total friction, 
and hence the total pull that can be 
transmitted, is 

^=T,-7; = 7;(e/«-i). . (1) 



2 



In a wire-rope transmission, the rope 
passes over two such wheels. If the 
wheels are of different sizes, or if the are 
of contract is not the same on both 
wheels, this computation must be made 
for both wheels; and the power which can 
be transmitted is equal to the lesser of 
the two frictions so found. Ordinarily, 
the conditions at the two wheels are iden- 
tical. If the wheels are allowed to come 
to rest, it is found that the tensions of 
the two free portions of the rope become 
the same, being equal to the mean of the 
tensions of the driving and following 
portions of the rope while in motion. 
The ratio which this mean tension bears 
to the force which can be transmitted 
when the wheels are in motion is 

In wire-rope transmission, the rope is in 
contact with one half the circumference 
of each wheel, or 6 = tc; and, for wire 
rope ri^nning on leather or hard rubber, 
f=z 0.26. The value of ef^ then be- 



73 



comes e * = 2.188; and the previous equa- 
tions become 

T T T 4- T 

^^ = 2.188; -^ = 1.84; -^ff^ = 1.34. ^ 

In practice^ it is usual to assume 

T 4-T 
^^^^ = 1.5^ 



. (3) 



Hence, the transmission of the force F 
with the linear velocity of the wheel-rim 
causes a direct tension T, = 2 i^ on the 
driving side of the rope. 

Let D = diameter of rope in inches, 
d = diameter of wire in inches, 
a = total cross-sectional area of 

wires, 
t^ = tension per square inch of 

wires (in driving side of 

rope) due to transmission 

of jR 

Then T^-t,a:=%F 

and a=^-^. 



74 



In the wire rope (Fig. 5) commonly used 
for this purpose, there are 43 wires and 

D = 9d; hence a = 42 — r— = -7 — ^ = 

0.4072 />'. Substituting this value of a 
in the expression just found, and solving, 
we have 

/)' = 4.9116 1^. . . (4) 

Let H= number of horse-power to be 

transmitted, 
E = radius of wheel in inches, 
iV= number of revolutions per 

minute. 

Then i^i _ 33000^ _ 198000^ 
~"27rRN~ nRN ' 

4.9116x1 98000 ff 



and Z) = 556.4i/_J?! ... (5) 

To find the value of D from this equa- 
tion, we must at- the very outset know 
what is the 'proper tension t^ to use in the 
ropes; and we must thus at once proceed 



76 



to determine the amount of the tensions 
due to bending and to centrifugal force, 
as these must be substracted from the 
total tension allowable in the rope to ob- 
tain the tension t^ which is available for 
the actual transmission of power. 

Bending Tension. — Passing to the con- 
sideration of the stresses caused by bend- 
ing round the wheel (Fig. 26), let 

R = radius of wheel in inches, 

d = diameter of wire composing rope 

in inches, 
E = modulus of elasticity of wire, 
t^ = tension per square inch of wires, 
caused by bending action. 

When the rope is compelled to bend to 
the curve of the wheel, the outer fibres 
of each wire will be extended and the 
inner ones compressed, while the center 
(the neutral axis) will remain unchanged 
in length. 

The length of the neutral axis of a wire 

subtending any angle or is A^ = ^^ R a. 
The outermost fibre of this wire subtends 



76 



the same angle with radius i? + -^ , its 

length being thus K—^[^\I^ + ^j^- 

The amount by which the outermost fibre 
has been extended is thus 

' ^ "" 180 • 2 • ^ ^ 

Fig. 26. 




and the extension per unit of original 
length is 

Ai 3 jB 



77 



TbBnrft'OTn-'tlig' defiiiitioii oT'Ehe modu- 
lus of elasticity, we have 

E "=1 t -^ = -' 

• • 2 i2 d ' , 

whence ^•~2~p' • • • (6) 

Prom these equations the tension may 
be determined. For the elasticity of 
iron wire we may take the mean of vari- 
ous experiments, viz., 28,000,000 lbs. 
Substituting this value of E and also 

introducing for d its usual value — -, we 

have for the tension per square inch 
caused by bending 

__ 280000 00 D 
h- iQj^ • • • (») 

Substituting in equation (8) some of 
the probable values of the ratio ^, we 
get the following table : 



78 











B 




B 




D 


u 


D 


^ 


40 


38888 


120 


12968 


45 


34570 


130 


11965 


50 


31111 


140 


11111 


55 


28282 


150 


10730 


60 


25925 


160 


9722 


65 


23930 


170 


9150 


70 


22222 


180 


8642 


75 


20740 


190 


8187 


80 


19444 


200 


7777 


85 


18800 


210 


7407 


90 


17284 


220 


7161 


95 


16874 


230 


6763 


100 


15555 


240 


6481 


110 


14141 


250 


6222 



For steel wire the modulus of elasticity 
would be about 30,000,000, and the values 

m 

of t^ would be proportionately higher. 

This table shows clearly the cause of 
the rapid wear of the ropes when running 

JD 

on small pulleys. When the ratio -j^ is 

large, the tension due to bending is small 
in comparison with the total allowable 
tension (see p. 81), and varies but slightly 
with small changes in this ratio; while, 
if the latter is small, the tension due to 
bending is not only a large proportion of 



79 



the total allowable tension, but in extreme 
cases is even greater than this tension. 

R 

On the one hand, as the ratio y de- 
creases, the wheels become smaller and 
less expensive; but on the other hand, 
we can get but little useful tension on the 
ropes, or if we increase the latter, the 
strain becomes so great that the ropes 
soon wear out. 

Centrifugal Tension. — Taking up the 
consideration of the tension due to the 
centrifugal action of the rope, let 
g = acceleration of gravity = 32.2 feet 

per second; 
to = weight of the rope in pounds per 

running foot; 
V = velocity of the rope in feet per sec- 
ond ; 
r = radius of wheel in feet; 
t^ = tension per square inch of wires due 

to centrifugal force. 
Then the centrifugal force is 



^ "" r ~~ g' r' 



i 



u 



IWVN^^^^ 



80 



-• 



and the total tension due to this centri- 
fugal force is 

In the 42 -wired ropes in ordinary use 
w = 1.5 /)•, andthe total cross-sectional 
area of wires is a = 0.4073 Z>'. 

Hence, for this rope, the intensity of 
this tension is 



^. = ^^ = 0.1144 1;», 



(9) 



being thus independent of the diameter of 
the rope. 

Substituting some of the probable val- 
ues of V, we have 



V 


■* 
•1 


V 


U 


80 


108 


70 


061 


40 


188 


80 


782 


50 


288 


90 


927 


60 


412 


100 


1144 



Total Tension. — While any transmis- 
sion is in operation, the rope is subjected 
to all three of the tensions previously 
considered. The actual and relative 



81 



amounts of these different tensions we 
may vary at pleasure, provided only that 
their sum {K^ = t^ -\- t^ + t,) does not 
exceed a certain amount, depending on 
the nature of the material of the wires. 

This maximum allowable intensity of 
tension may be taken rather higher in 
wire rope than when the material is used 
in larger masses, as wire-drawing is itself 
a process of testing and selection, only 
high grades of iron being capable of being 
drawn into wire. 

For iron wire rope it is safe and cus- 
tomary to take K^ = 25,600 pounds per 
square inch of wires ; while for the 
special grades of cast-steel ropes we may 
go as high as 50,000 pounds. It is, 
however, generally better in the case of 
steel ropes not to go very much above 
the usual limit for iron, and to employ 
the superior strength of the steel rope, 
not to transmit a greater force, but to 
enhance the durability of the rope. 

In apportioning the total tension into 
its three components, we first estimate 
the speed at which the ropes are to run 
and deduct the tension, ^„ due to centri- 



L 



} 



82 



fiigal force at that speed, from the whole 
tension, -ff,/ In all ordinary cases we 
need not for this purpose estimate the 
exact speed, but may assume t^ = 600 
pounds, so that we will then have for iron 
Tope a tension -K^= ^, — 600 = 25,000 
pounds per square inch to divide between 
t^ and i^. 

The principal conditions determining 
the best relative values of t^ and t^ are 
two in number — (1) the size of wheel that 
may be conveniently employed, (2) the 
resulting deflection or sag in the ropes; 
the latter being again subject to various 
conditions, such as the available height, 
distance between wheels, etc. 

Combining equations (5) and (7) we 
get 

_ 30955 E' H 1 
324 iV • tX' 

The condition under which the value of 
jB is a minimum is obtained by placing 
the first differential coefficient of this 
equation equal to zero, which gives 



U-^Kl • • • UO) 



83 



in other words^ in the case most favorable 
to small wheels the tension caused by 
bending is twice as great as the direct 
tensional strain, and is hence, of course, • 
/, = I ^ where K = 25,000. 

As a rule, it is advisable to use a wheel 
considerably larger than would be given 
under such conditions, and the best prac- 
tice .seems to indicate, as most suitable, 
a value t^ = t^ = 12,500, which corre- 
sponds to about B = 125. Making prop- 
er substitutions in equation (5) we have 

i> = 0.583 y^, . . (11) 

and the diameter of the corresponding 
wheel in inches is 

({/,>■ ■= 2B = UQ\/^.. . (12) 

The diameter of wheel given by equa- 
tion (12) agrees fairly well with that used 
in practice; but the ropes are usually 
made from ^ to J inch larger in diameter 
than given by equation (11), both for the 
sake of enhancing the durability of the 
rope, as well as to counterbalance the 
effect of stretching by giving the rope an 



a-<. \. 






i 






} 



84 



initial tension greater than the normal 
working tension. 

We now pass to the consideration of 
the causes directly producing the tension 
ti, and the manner of fixing its proper 
amount in any actual case. 

The Catenary. — If a perfectly flexible 
rope be secured at two points and loaded 
continuously between them according to 
any law, it will assume some definite 
curvilinear form. When the load is the 
weight of the rope only, the curve is 
called a catenary. 

Suppose that the rope is fixed at the 
points A and B (Fig. 27), and that the 
only force in operation is the weight of 
the rope, i.e., the load is a continuous 
and direct function of the length of arc. 
Take the origin of co-ordinates at C, the 
lowest point of the curve, and let the 
axes of X and y be horizontal and ver- 
tical respectively. 

Let ti = tension at any point a; 
t^ = tension at origin 6'; 



85 



< 



Is 




86 



I = length of curve a C; 
L = total length of curve between 

supports A B; 
to = weight of rope in pounds per 

running foot; 
S = span between supports; 
J = total deflection or greatest 
ordinate of curve. 
Then the point a is kept in equilibrium 
by the tension t' and the applied forces 
between C and a. These applied forces 
are the tension t^ acting horizontally at 
C, and the weight of the rope, w I, act- 
ing vertically along a 0. 

Resolving vertically and horizontally, 
we have as the equations of equilibrium, 

r^=., . . . (13) 

t'i^=wl . . (U) 
dl 

Thus ':he horizontal component of the 
tension at any point a is equal to the ten- 
sion at the lowest point, i,e,, the horizon- 
tal component of the tension is constant 
throughout the curve; and the vertical 
component of the tension at any point is 



87 

eqnal to the weight of so much of the 
Tope as comes between the origin and the 
point considered. 

Diriding equation (14) by equation 
(13), we get, for the tangent of the angle 
which the rope at any point a makes with 
the horizontal. 

Differentiating eqaation (15), we have 

but dl = {dx* + dyy = (l + ^Y<^- 

SubstitutiDg this value, we have, after 
transposiDg, 

^rf«,= J^ . (16) 
Integrating equation (16) we obtain 



i 



88 
which may be written 



wx 



e'.=^-y + /l+% . (17) 

ax dor ^ ' 

where e is the base of the Naperian sys- 
tem of logarithms. 

Transposing, squaring, and simplify- 
ing equation (17), we get 

dy = i\e io -e *• Ydx. (18) 

Integrating the above equation between 
any point {x, y) and the origin, we have 

which is the equation of the catenary. 
To bring this equation into a somewhat 
simpler form, we transfer the origin of 

co-ordinates to Ci , making C Ci = - . 

This line C Ci is called the parameter of 
the curve. Then our new ordinates will 

be ^0 = y + - ; so that equation (19) may 

be written 

J. t wx — wx \ 



89 



Bnt this change of origin evidently does 

d V 
not affect the value of -r^ , the tangent 

ax 

of the angle a ; and substituting ^ = — 

from equation (15) in equation (18) we 
obtain^ for the length of arc, 

I f vox —tox \ 

Subtracting the square of equation (21) 
from the square of equation (20), we have 



7 — i/y ^ ^tZ. 



and the whole length of the rope between 
supports, for which ?/„ = J + - , is 



= Wr ■^^^' 



Z = 2yj»+^l^-\ . (23) 

This equation gives the means of com- 
puting the length of the rope when, in 
addition to the deflection, the running 

weight of the rope and the ratio - are 

I . 4 . 



i 



90 



1' 



has its least value at the lowest pointy 
where 

and it reaches its maximum value at the 
points of support, where 

t'^^wAJ^t,, . . (27) 

being thus equal to the tension at the 
lowest point, plus the weight of a piece 
of rope whose length is equal to the de- 
flection. The smaller the deflection of 
the rope, the less is the difference between 
^'ma» and Z^. When J = 0, we have 
t' = t^-= infinity, showing the impossi- 
bility of stretching a rope so as to be per- 
fectly horizontal. The vertical compo- 
nent of the tension at each of the points 
of support is of course equal to the weight 
of one half the rope. That is. 



the horizontal component of the tension 
at the point of support being t^ , as al- 

rgady.detfirmined , .. — 

f The angle which the curve at the point 



^' • -• . ... 



.c 



91 



• ' I ( < I 



known. The value of w is always known 
in any particular case, and for the 42- 
wiredrope usually employed w = 1.5 D*. 

The value of the ratio — , as obtained 

w 

by solving equation (20), for either point 

of support, is 

L A^ (24> 

^ "" wS -wS • • V* / 

Its value depends thus directly on the 
relation between the deflection and span, 

being very large where ^ is small, as it 

always is in the transmission of power by 
wire rope. 

For the tension along the rope at any 
point, we have 



— wy,i ...... (25) 

being thus directly proportional to the 
, weight of the rope per running foot. It 



1 



92 



of support makes with the horizontal is 
given by 

tana] = 07 = 7"^ "^ +"^ • (^^) 

Approximate Equations of Catenary. — 

In practically applying the preceding 
equations, we meet with considerable dif- 
ficulty, owing to the fact that the para- 
meter — can only be obtained, from a 

transcendental equation. 

But in such work as forms the subject 
of this volume, we can pursue a fre- 
quently used method of approximation, 
which is abundantly accurate for all our 
purposes. The exact equations of the 
catenary, as we have deduced them, are 
of course applicable ; but as we have left 
the stiffness of the rope out of considera- 
tion, and assumed it to be perfectly flex- 
ibUy the properties of the curve are not 
expressed with mathematical exactness 
by even these equations. For this reason 
alone, it might be permissible to use ap- 
proximate formulae; but we have a still 
greater right to use them, because the 



93 



deflection A is always a very small frac- 
tion of the span 8^ and therefore the 

parameter — is always very large. 

Consequently, in equation (24) the 
exponents of e are small fractions, and 
we may express their values by the con- 
verging series 

^ ^*' 2X^2X4C 3X3X8C"^ 

Taking the first four terms of these 
series, and substituting them in equa- 
tion (24), we get 



t, _ 2J 
10 ~~ w' /S" 




4/«' 





(30) 



A similar modification of equation (20) 
gives 






4^' 



i 



94 

hence 

8* wx* ,„,, 

^«-8J=T^ <'1> 

This is the equation of a parabola hav- 

era 

ing a parameter of j-.; so that our meth- 
od of approximation has led us to con- 
sider the curve as a parabola. 

Making these substitutions throughout, 
the previously deduced exact formulas 
now become 

t'max = w(j + -^y . (32) 



tan«]^ = -^i/j' + 4^. . (35) 



S" '4 



L= 3|/j'+|l. . (36) 

Equation (36) is equivalent to assum- 
ing that the length of the curve between 



f . •• 



/ ' 96 ^. 

r 

either point of support and the lowest 
point is equal to the straight line joining 
those points. In using this equation^ it 
must further be noted that the length of 
the actual rope after splicing must be 
2 Zl 'x; ;r p . wh«?n J is the deflection at 
rest. ^^j^ pf lC3> 

Practical Deductions. — It must be re- 
membered that t'nax is not the maximum 
tension per square inch of wires, but the 
total maximum tension on the rope, being 
in fact the same as the tension 7\ or T^ , 
previously considered, for the driving 
and following sides respectively. Mak- 
ing our usual assumptions as to weight 
of rope per running foot, and relative 
diameters of wire and of rope, we find 
that for the common 42-wired rope the 
maximum tension per square inch is 



~ a a\ "^ 8"2l. 



= 3.684(^ + ^2)' • • (^^^ 

being thus independent of the diameter 
of the rope. For different varieties of 



96 



rope, the numerical constant would of 
course vary somewhat, and can be readily 
obtained for any case. 

As we liave previously seen, this ten- 
sion is different in the driving and fol- 
lowing portions of the rope while the 
latter is in motion, and has the same in- 
termediate value in both sides of the 
rope while at rest. 

A convenient way of practically ascer- 
taining the tension of the rope at any 
time is by means of a vertical staff set in 
the ground near the lowest point of the 
rope. The staff beini^r graduated by the 
formulae found for the relation between 
tension and deflection, the tension can 
at any time be read off by simply sight- 
ing across the rope to the graduations on 
the staff. 

In order that the rope may be sub- 
jected to its proper tension while in 
motion, the deflection or sag must be of 
a certain magnitude while the rope is at 
rest ; we must also know the sag of the 
driving and following sides while in 
motion, in order to estimate the necessary 
elevation of the wheels. There are there- 



97 



fore three deflections to be determined : 
J, , that of the driving side in motion; 
A^ , that of the following side in motion; 
A^ y that of both sides at rest. 

We must know the deflection at rest, 
A^y in order to determine the proper 
length of rope ; so that when it is put on 
and spliced, we may feel certain that 
there will be neither any slipping during 
the motion, nor any over-straining of the 
rope itself. The deflections J, and J, 
must be known, in order to determine in 
advance what position the ropes will take 
while in motion, how near they will ap- 
proach the ground or other obstructions, 
and how many, if any, carrying-sheaves 
are required. 

Solving equation (37) for J, we get, 
for the value of the deflection, 

A - 0.1357 {t - Ve - 6.785 fif*). (38) 

The deflection of the driving side will 
be the least, and is 

-^1= 0.1357 {t, - f/^- 6. 785^5'). (39) 



L 



98 



where t^ \&, as usual^ the tension per 
square inch of wires (in driving side of 
rope) due to the transmission of F. 

The deflection of the following side 
and the deflection at rest are similarly 
found by substituting in equation (38) 
the values ^ = ^ /, and ^ = J ^^ respect- 
ively. Thus we have 

J,= .0679 (/,- f'//- 27.15 6^0;. (40) 
J,= .1018 {t, - VC- 12.06/^0. . (41) 

In all ordinary cases, where the fol- 
lowing portion of the rope is below, the 
deflection of this side is the most import- 
ant, as the necessary height of the 
wheels is thereby determined. This 
height must be so adjusted that the low- 
est portion of the rope will never touch 
the ground. Hence, assuming the ground 
to be level, the height of the center of 
the wheels above the ground must be at 
least i? + J, , and should in practice be 
made somewhat greater to allow for the 
stretching of the rope. If the ground is 



99 



not level, or if there are obstructions, 
this height must be varied accordingly. 

To give a better idea of the relative 
magnitude of the quantities involved, I 
have computed, by means of equations 
(37) and (38), the following tables, 
which will also be found useful as a first 
approximation in designing: 

TENSION 

PER SQUARE INCH OP WIRES FOR VARIOUS 
SPANS AND DEFLECTIONS. 



ction 

eet, 


SPAN IN FEET. 


Defle 


100 


200 


300 


400 


500 


H 


18,420 


73.630 


165,800 


294.720 


460.600 


x2 


9,210 


36,820 


82,900 


147,380 


280,300 


1 


6,140 


24.570 


55,250 


98,250 


153,500 


4,610 


18,420 


41,450 


73.680 


115.150 


s 


2,310 


9,220 


20,730 


86,850 


57.580 


3 


1,550 


6.150 


13.830 


24..570 


38,390 


4 


1,166 


4,620 


10,380 


18,480 


28.800 


5 


940 


3,700 


8,310 


14,750 


23,050 


6 


T90 


3.090 


6,930 


12,800 


19,210 


7 


685 


2.650 


. 5,950 


10,550 


16.470 


8 


605 


2,330 


5,210 


9,240 


14,4-^ 


9 


545 


2.080 


4,640 


8,220 


12,826 


10 


495 


1,880 


4,180 


7.400 


11 550 


12 


465 


1.580 


3,678 


6.223 


9.640 


15 


362 


1,283 


2,818 


4,966 


7,732 


90 


304 


995 


2,146 


3.768 


5.832 


85 


2T6 


829 


1,750 


3,040 


4,697 



» J' - 

m .J •* 



100 



DEFLECTIONS, 

IN FBBT, CORRESPONDING TO VARIOUS TEN- 
SIONS AND SPANS. 



Tension, 




SPAN IN FEET. 




per 

• mm 












square inch 












of Wires. 


100 


200 


800 


400 


600 


26,000 


.19 


.72 


1.66 


2.99 


3.26 


20.0IK) 


.23 


.92 


2.06 


8.68 


5.77 


17.S00 


.27 


1.06 


2.43 


4 21 


6.51 


15,000 


.32 


1.24 


2.77 


4.94 


7.68 


12.500 


.38 


1.48 


3.31 


588 


9 28 


10.000 


.46 


1.84 


4.21 


7.40 


11.56 


7.600 


.61 


2.46 


5.53 


9.85 


15.44 


5,000 


.92 


3.69 


8.35 


16 26 


23.42 


4,000 


1.15 


4.63 


10.46 


18.74 


29.57 


8.000 


1.53 


6 20 


14.03 


25.34 


40.35 


2,000 


2.31 


9 36 


21.58 


39.74 


65.40 


1,000 


4.68 


19.89 


51.04 






750 


5.97 


28.57 








500 


9.94 











The blank spaces in this table indicate 
that the respective combinations are im- 
possible. There is, in fact, for each span 
a certain deflection at which the tension 
has its minimum value ; so that any fur- 
ther increase of deflection bevond this 
point cause the tension again to increase, 
until finally both reach infinity together. 
Though this minimum tension and its 
corresponding deflection are entirely out 
of the range of ordinary practice, it will 



101 



nevertheless be of interest to determine 
their values. Differentiating equation 
(37) we have 



J^ = 3.684 (1 



(' 



8JV' 



which being placed equal to zero, gives 

A = 0.3536/5 
as the deflection corresponding to the 
miDimum tension, the value of the latter 
being 

For the spans of the foregoing tables, we 
obtain the following values : 



Span in Feet. 


Minimum Tension 

per Square Inch 

ofWires. 


CorreRponding 

Deflection 

in Feet. 


100 

aoo 

300 

t400 

500 


S60 

520 

780 

1040 

1800 


35 36 

70.72 
106.06 
141.44 
17G.80 



Examples. — Suppose for instance that 
it is required to transmit 300 horse-pow- 
er over a distance of 200 feet, and that 
we are to put our first wheel on the 
main shaft of a steam-engine making 100 
revolutions per minute. Equations (11) 



102 



and (12) would give us /> = 0.84 and 
2 i? = 210, so that we should employ a 
y rope over a wheel 17^ feet diame- 
ter. In all probability this wheel would 
be larger than would be convenient; in 
which case it would be advisable to use 
two ropes running side by side and each 
transmitting one half the power. For 
such an arrangement, we would find 

i) = .67 and 2R = 168, 

so that we should employ two ^" ropes 
running over 14-foot wheels. 

The force to be transmitted by each 

,, , 33000 X 150 ^^_ 

rope would be — — -- = 1125 

^ TT X 14 X 100 

pounds ; and the area of the wires in 
the rope is 0.4072 D^ = 0.1*2 sq. inch. 
Hence, while at rest, the tension per 
square inch in both sides of the rope will 

be - — -^ — ■'- = 8796 pounds ; while in 

motion, the tension on the driving side 

2 X 1125 
will be ;vio~~ ~ ll'^28 pounds, and on 

1125 

the folloiving side — ^ = 5864 pounds. 



103 



Interpolating in table on p. 100, we 
find the deflection of both sides of the 
rope at rest to be about 25^ inches ; 
while in motion, the deflections of the 
driving and following sides will be about 
19 and 39 inches respectively. 

If greater exactness is required, the 
deflections may readily be calculated by 
means of the formulae previously given. 
Allowance muet always be made for the 
stretch of the rope, which increases the 
necessary height of wheels above ground. 

The necessary length of rope after 
splicing is found by means of equation 
(36) and is 



2L+ 27tR = 4|/jo«+ ^ +44 

= 444 feet. 

If the rope, as above calculated, be just 
large enough to transmit the required 
power at the given deflection, it will no 
longer do so after stretching, on account 
of the decrease in tension accompanying 
the increased deflection due to stretch- 
ing. This can only be avoided by re- 
splicing the rope as soon as the in- 



104 

creased deflection becomes perceptible, 
by refilling the wheel as previously ex- 
plained, or, still better, by using a rope 
somewhat larger in diameter than found 
from eq. (11), giving to it a deflection 
corresponding to a greater tension than 
we need, thus allowing a margin for the 
decrease of tension accompanying in- 
creased deflection. 

To illustrate, let it be required to 
transmit 50 horse-power at 80 revolu- 
tions. Equations (11) and (12) would give 

D = 0.498 and R = 124.8. 

Taking an 11-foot wheel as the nearest 

larger wheel in the market, we would 

find the force to be transmitted to be 

33000 X 50 _- , T* 

t:: 7^ = 469 pounds. If we were 

TT X 11 X 80 ^ 

to use a ^-inch rope, as given by equa- 
tion (11), we should have tension per 
square inch of both sides at rest 6900, 
tension on following side 4600, and on 
driving side 9200 pounds. Supposing 
the distance of transmission to be 300^ 
feet, the greatest deflection of the driv- 
ing side, when just able to transmit the 



105 



force, would be about 4.6 feet. But as 

-g = 130, we should have t^ = 11965 

and the maximum allowable value of 
t^ = 25000 - 11965 = 13035, so that we 
could start work with a deflection of only 
3.2 feet ; and the power would be trans- 
mitted until the stretch had caused the 
deflection to exceed 4.6 feet. 

We might do still better by employing 
a f" rope, in which the tension per 
square inch on the driving side would 
only be 7256 pounds, corresponding to a 
deflection of about 5.8 feet. In this case 

R 

J. = 114, corresponding to t^ = about 

13600. We should thus have a maximum 
value of t^ = 25000 - 13600 = 11400, 
corresponding to a deflection of about 
3.7 feet; so that the transmission would 
work satisfactorily while the deflection 
of the driving side underwent a varia- 
tion of over two feet. 

Similarly, in the first example above 

, R 84 X 16 ,-^ 
given, we have ^ = — — — = 122, cor- 
responding to about ti = 12750, and the 



106 



maximum value of t^ = 25000 — 12750 
= 12250, so that we could start with a 
deflection for the driving side of 18 
inches, giving us 1 inch deflection to 
spare for stretching. A similar advan- 
tage would result in this case from the 
use of the next larger size of rope. 

The relative and absolute sizes of 
wheels and ropes in any actual case may 
of course be considerably varied accord- 
ing to the designer's judgment, the only 
absolute condition being that t^ + t^ 
shall not, for iron ropes, exceed 25000 
pounds. As a safe general rule, it may 
also be stated that the wheel should al- 
ways be made as large as convenient. 

The practice of one of the representa- 
tive American firms is shown by their 
table on the following page. 

As will be evident by computing any 
of the cases given in the table, a liberal 
margin has been allowed for any tem- 
porary increase of work or diminution 
of tension by increased deflection, and 
for the wear of the ropes. 



107 



Diameter 

of 

Wheels 

in feet. 



8 

4 

5 

6 

7 

8 

9 

9 

10 

10 

12 

12 

12 

14 

14 



Diameter 

of 
Rope in 
inches. 




HoRSs-POWBR Traksmittbd at— 



8 

4 
9 
14 
20 
26 
47 
48 
64 
6H 
93 
99 

i4i* 

148 



100 


120 


Revs. 


Revs. 


8i 


4 


5 





11 


18 


17 


20 


25 


80 


82 


89 


58 


60 


60 


78 


80 


96 


85 


102 


116 


140 


124 


149 


• • • • • 


178 


176 


• • • • 


185 


• ■ ■ • 



140 
Revs. 



I 

16 
28 
86 
45 
82 
84 
112 
119 



Special Cases. — The lower side of the 
rope is nearly always the folloioivg side ; 
but if there is any difficulty about secur- 
ing the necessary height to provide for 
the deflection of the following side while 
in motion, we may make the lower side 
the driving side, in which case the deflec- 
tion at rest is the greatest to be provided 
for. 

When in motion (fig. 28) the lower 
driving side rises above its position at 
rest, and the upper side sinks, thus en- 
abling us to avoid obstructions, which 



109 



by the other way would have to be re- 
moved. Of course this expedient can- 
not always be employed, as the upper 
side of the rope must not be allowed to 
sink so far as to pass below or even to 
touch the lower side. If this occurs, the 
rope begins to sway and jerk in a serious 
manner, wearing out very rapidly. 

The shortest distance between the ropes 
is 2 i? — (Jg — -^i). We must there- 
fore always be careful, in using this 
plan, to see that 2 iZ > /d^ — ^^, which 
result may be obtained by a judicious se- 
lection of the tension, and of the diame- 
ter of wheel. 

The spans which may be used in prac- 
tice are limited in one direction by the 
steadily increasing tension and deflec- 
tion, and in the other by our inability to 
secure the necessary tension without 
special tightening devices. 

The maximum limit has been already 
considered, and depends on local circum- 
stances, being usually from 300 to 500 
feet. The minimum limit may readily 
be obtained from equation (33), assum- 
ing that the deflection shall never be less 



110 

than 18 inches, and that t^ shall never 
exceed 500 w. We then have 



S= i/s J ^ = 78 feet. 
^ w 

Below this distance, shafting will usu- 
ally be found preferable and less trouble- 
some. 

It sometimes happens that the two 
wheels are not at the same height, as 
has been hitherto supposed, but that one 
is at a higher level than the other. This 
frequently happens where it is desired to 
use the power of waterfalls in a ravine, 
or in conducting power up or down the 
side of a hill, the rope taking a position 
such as is shown in Fig. 29. 

If the difference in height is slight, we 
can use the formulas already found, with- 
out introducing any serious error. If the 
rise be considerable, however, the ten- 
sion of the rope at the upper wheel will 
be greater than that at the lower. In 
this case, the power which can be trans- 
mitted depends only on the tension at 
the lower wheel, which may, if desired, 
be made smaller than the upper wheel, so 



Ill 



Ik 




112 



that the total tension in the rope in go- 
ing round each wheel shall be the same. 
The total span being S, and the differ- 
ence in level of the two ends A, then, by 
the known properties of the parabola, 
we have, for any deflections J^ and J, 
(see Fig. 29), __ 



/Si = /S 



= S 



VA + VA 

VA 



VA+ Va + A' 



Assuming any convenient value of Ji , 
we make all the calculations for the 
lower wheel as though the span were 
2 Si , and for the upper wheel as though 
the span were 2 /Sg • If ^^ results are 
not satisfactory the first time, a few suc- 
cessive alterations of A^ will readily give 
the desired results. 

The readiest and most usually em- 
ployed method of getting the value of 
Si is the following : An accurate scale- 
drawing is made of the plan in which 
the rope is to be placed. This drawing 
is set vertically, and a fine chain is fas- 



113 



tened or held with its two ends at the 
points of support until a proper deflec- 
tion is obtained. It then becomes a matter 
of ease to measure Si and S,, and to 
make all the necessary calculations. We 
can in this way try different deflections 
and observe their suitability to the design, 
but must always bear in mind whether 
we are getting the deflection of the driv- 
ing or of the following side or that of 
both sides at rest. This method, though 
not giving as great accuracy as the so- 
lution of the above equation, is neverthe- 
less largely used in practice, owing to its 
great convenience. It may be used when 
the pulleys are on the same level, show- 
ing between what limits we may work. 

Another peculiar case is when the rope 
rises nearly in a vertical direction. This 
is the limiting case of the inclined trans- 
mission. The rope produces no tension 
whatever on the lower wheel, while at 
the upper wheel the tension is only 
equal to the weight of the rope. Even 
this last tension is such a small quantity 
as to be left entirely out of considera- 
tion, and we are consequently obliged to 



114 

use some device for producing the re- 
quisite tension, such as the tightening- 
sheaves shown in Figs. 30 and 31. In the 
latter, the rope passes around the wheel 
twice, so that the wheel must be pro- 
yided with two grooves. 

Fig. 30. 




The requisite tension in the vertical 
ropes may also be obtained as shown in 
Fig. 32, by running them over two carry- 
ing-sheaves at the upper point and in- 
troducing a sufficient horizontal span 



116 

the deflection of which corresponds to the 
tension desired. 

Pressure on Bearing. — A simple graph- 
ic method of finding the pressure on 

Fig. 31. 




the wheel-bearings, and hence also the 
direction of the thrust on the supports, 
is shown in Figs. 33 and 34. Let Fig. 
33 show the tensions on the ropes on a 



1 



116 

Fi9- 31. 





117 



double-grooved wheel at an intermediate 
station. Draw (Fig. 34) AB,B C, D C, 
D E respectively parallel to, and on some 
convenient scale proportional to, T, T^, ty 

Fig. 33. 




and ^j. Draw EF vertical and represent- 
ing on the same scale the weight of 
wheel and shaft. Then A F will on the 
same scale represent the intensity and 



118 



direction of the thrust on the bearings. 
If we had been considering an end sta- 

FSg. 34. 

! 

I 




tion the distances B C and D E wonld 
have been zero. 



119 



EFFICIENCY. 

Other things being equals the relative 
merit of various methods of transmitting 
power will be indicated by the cost of 
transmitting a certain amount of power 
to any given point, as compared with the 
cost of this power at the generating sta- 
tion, while their absolute merit will be 
shown by comparing the cost of the 
transmitted power at the receiving sta- 
tion with the cost of producing the re- 
quired power directly at this point. 
Such determinations are materially af- 
fected by variations in the amounts of 
power and in the distance of transmission, 
the other principal factors to be consid- 
ered being the efficiency of the system, 
the number of working hours per annum, 
the price of one horse-power per hour at 
the generating and receiving stations, 
and the convenience and applicability of 
the system to each special case. 

The efficiency of any system of trans- 



120 

mitting power is expressed by the ratio 
of the power obtained at the receiving 
station to the power given out at the 
generating station. In all systems^ losses 
of power of greater or less magnitude 
occur, and the most eflficient system is 
that in which those losses are reduced to 
a minimum. 

In the transmission of power by wire 
ropes, the causes which tend to thus 
waste a portion of the power in doing 
useless and even prejudicial work are — 

1. The rigidity of the ropes in bending 
to the curve of the main wheels and carry- 
ing-sheaves. (The loss from this source 
may usually be regarded as insensible ; 
for when the wheels are made sufl&ciently 
large, the wires of the rope straighten 
themselves by their own elasticity after 
leaving the wheels) ; 

2. The friction of the journals of the 
wheel-shafts ; 

3. The resistance of the air to the ro- 
tation of the wheels and to the passage 
of the rope through it. 

The friction of the journals varies di- 



121 



rectly with the pressure on the bearings, 
while the resistance of the air depends 
only on the velocity of the wheels and 
ropep. The losses due to both these 
causes have been experimentally deter- 
mined in a number of cases. It must 
be noted that, as the pressure on the 
bearings depends only on the tension 
and deflection of the rope, which with 
a given velocity of wheels are constant 
irrespective of the power transmitted, it 
follows that these losses are to a large 
extent independent of the transmitted 
power. When the direct tension due to 
the latter is small compared to the ten- 
sion due to the span and deflection of 
the rope, these losses will become of 
considerable relative magnitude, so that 
it is a condition of efficiency that the sys- 
tem shall be worked at the highest suit- 
able power. Under such circumstances, 
the efficiency of a single pair of stations 
has been determined to be 0.962 ; so that 
the efficiency of any whole system in- 
cluding a certain number of intermedi- 
ate stations is as follows : 



122 



Number of 

Intermediate 

Stations. 


Efficiency of 
System. 


Per cent of 
Power Wasted. 



1 
2 
3 
4 
5 


0.962 
.944 
.925 

.908 
.890 
.873 


8.8 
5.6 
7.5 
9.2 
11.0 
12.7 



The efficiency is thus seen to be very 
high for ordinary distances, and, for any 
given distance, it will be greater the fewer 
the number of intermediate stations. 

One of the best recently published 
comparisons of the four principal sys- 
tems that may be employed for trans- 
mitting power to distances is to be found 
in Beringer^s *' Kritische Vergleichung 
der Elektrischen Kraftiibertragung^* 
(Berlin, 1883). On the basis of many 
experimental determinations, he has com- 
puted the following table as representing 
the commercial efficiency of the different 
systems under various conditions of dis- 
tance and power, all the systems being 
supposed to be working to the best ad- 
vantage : 



123 



COMMERCIAL EFFTCIENCY. 



IMstance of Trans* 


Elec- 


Hy- 


Pneu- 


Wire 


mission in feet. 


tric. 


draulic. 


matic. 


Rope. 


300 


.69 


.50 


.55 


.96 


1.500 


.68 


.50 


.65 


.93 


3,000 


.66 


.50 


.55 


.90 


15,000 


.60 


.40 


.50 


.60 


30,000 


.51 


.35 


.50 


.36 


60,000 


.33 


.20 


.40 


.13 



It will be seen from this table that wire 
rope is most efficient up to about three 
miles, beyond which electric and pneu- 
matic transmission are most efficient. 

The cost of erecting and operating 
6uch transmissions varies greatly accord- 
ing to local circumstances. For wire- 
rope transmissions, the prices of ropes, 
wheels, and linings previously given will 
assist in its determination for any special 
case. In France, where by far the greater 
number of applications of this method 
have been made, the average cost of the 
plant and its erection is estimated at 
about $1600 per mile, with about $5 per 
horse-power additional for the necessary 
constructions at the termini. 



124 

Beringer enters at length into the mat- 
ter of cost, taking up in detail the capi- 
tal outlay required for various distances 
and amounts of power, each of the sys- 
tems being supposed to be worked in.the 
most economical manner. 

We need not follow him in the details 
of his many calculations, in which he con- 
siders thoroughly the practical bearings 
of the subject, but his final conclusions 
are full of interest. 

The following table gives the probable 
capital outlay required to establish trans- 
mission plants under the circumstan- 
ces given. These figures do not include 
buildings, boilers, chimneys, and cost of 
prime mover, as they are taken into ac- 
count in the cost of producing one horse- 
power per hour, but include all other 
expenses. 

From this table it will be seen that for 
distances less than about one mile the 
cost of the plant for wire-rope transmis- 
sion is less than that for any other sys- 
tem, and specially so as the power to be 
transmitted increases in amount. For 
powers greater than 100 H. P., its cost is 



125 



less for any distance not exceeding three 
miles. 



CAPITAL OUTLAY, IN DOLLARS, PER 
HORSE-POWER. 



Maximum 
Horse- 
power 
Trans- 
mitted. 



10 



60 



100 



Distance 
of Trans- 
mission, 
in feet. 



300 

1,500 

3,000 

15,000 

30,000 

60,000 



300 

1,500 

3,000 

15,000 

80,000 

60,000 



300 

1,500 

3,000 

15,000 

30.000 

60,000 



800 

1,500 

3,000 

15,000 

30,000 

60,000 



Elec- 


Hy- 


Pneu- 


tric. 


draulic. 


matic. 


365 


200 


355 


m) 


321 


468 


3ft4 


472 


1,020 


536 


1,740 


2,920 


G91 


2,970 


5,300 


i,oao 


6,230 
146 


10,000 


253 


292 


263 


219 


350 


273 


317 


429 


375 


1,070 


1,040 


502 


2,030 


1,800 


750 


3,920 


3,310 


195 


78 


151 


200 


101) 


175 


2a5 


146 


205 


SfiS 


443 


428 


ma 


828 


716 


487 


1,580 


1,290 


156 


68 


127 


Ifil 


97 


146 


170 


136 


166 


219 


429 


326 


287 


799 


531 


424 


1,510 


935 



Wire 
Rope. 



32 

151 

297 

1,480 

3,700 

5,940 



25 

112 

229 

1,125 

2,240 

4,550 

85 

68 

386 

•62 

1,824 

21 

41 

200 

394 

78» 



In comparison with electric trans- 
mission, which is practically its only 
competitor for long distances, we have 



i 



126 



already seen that, while the commercial 
eflBciency of wire ropes is much greater 
than than that of electric transmission 
for short distances, it rapidly falls and 
becomes less than that of the latter as the 
distance increases. The true comparison 
of the various systems must of course in- 
volve both capital outlay and commer- 
cial efficiency; in other words, the figure 
of merit for each system is the price 
which must be paid for one horse-power 
at the receiving station. 

To obtain this price, the assumption 
is made that the average cost of one 
horse-power per hour at the operating 
station is in 

Steam-engiDes of more tban50H.P. . 2.07 cts. 

" from 10 to 50 H.P. . 5.84 cts. 
" less than 10 H.P. . 7.71 cts. 

while the average cost of one horse-power 
in water-power varies from 0.2 to 0.4 cent 
per hour. 

Taking into account the figures for ef- 
ficiency previously given, and allowing 
14 per cent of the capital outlay for in- 
terest and depreciation, the following 
tables represent the cost of power at the 



r 



127 

receiving station, the power transmitted 
being supposed in each case to be gen- 
erated at the cheapest of the above 
rates : 

STEAM-POWER TRANSMITTED. 

FRICE, IN CENTS, OP ONE HORSE-POWER PER 
HOUR AT RECEIVING STATION. 



Maximum 
Horse- 
power 
Trans- 
mitted. 


Distance 
of Trans- 
mission, 
in feet. 


Elec- 
tric. 


Hy. 
draulic. 


Pneu- 
matic. 


Wire 
Rope. 


5 


300 

1,500 

8,000. 

15,000 

30,000 

60,000 


4.6 
4 7 
4.9 
6.8 
6.7 
10.5 


5.1 

5.8 

6 4 

13.2 

21.3 

38.5 


5.6 

6.0 

6.7 

10.6 

19.3 

33.9 


2.3 

2.9 

3.8 

11.0 

21.1 

46.0 


10 


300 

1,.500 

3.000 

15.000 

30,000 

60,000 


4.0 
4.2 
4.3 
5.1 
6.3 
9.8 


4.8 

5.2 

5.7 

10.3 

15.6 

29.0 


5.1 
5.4 
5.8 
9.1 
12.7 
21.1 


2.3 
2.8 
3.5 
9.1 
17.2 
38.7 


50 


300 

1,500 

3,000 

15.000 

30,000 

60,000 


3 a 

3.9 
4.0 
4.6 
5.6 
8.6 


3.3 
3.4 
3.6 
5.9 

8.5 
15.8 


4.1 
4.3 
4.4 
5 8 
7.2 
10.7 


2.2 
2.4 
2.6 
5.1 
9.1 
22.5 


100 


300 

1,500 

3.000 

15.000 

30,000 

60,000 


3.6 
3.7 
3.9 
4.4 
5.3 
8.3 


3.3 
3.4 
3.6 

5.8 

8.4 

13.9 


4.0 
4.1 
4.2 
5.3 
6.3 
9.1 


2.2 
2 3 
2.5 
4.5 

7.8 
19.7 



128 



WATER-POWER TRANSMITTED. 

PRICE, IN CENTS, OF ONE HOR8E-FOWER PER 
HOUR AT RECEIYINO STATION. 



Maximum 
Horse- 


Distance 
of Trans- 


Elec- 


Hy. 


Pneu- 


Wire 


power 
Trans- 
mitted. 


mission, in 
feet. 


tric. 


draulic. 


matic. 


Rope. 




aoo 


0.71 


0.59 


0.81 


0.22 




1.500 


0.78 


0:77 


0.95 


0.88 


5 


8,000 


75 


0.97 


1.17 


0.61 


15,000 


0.89 


2.79 


2.67 


2.6-i 




80,000 


1.05 


5.06 


4.86 


6.06 




60,000 


1.70 


9.70 


9.01 


9.84 




800 


0.54 


0.50 


0.71 


0.18 




1,500 


0.56 


0.61 


0.77 


0.34 


10 


8,000 


0.58 


0.75 


89 


0.60 


16,000 


0.78 


1 92 


1.78 


1.94 




80,000 


0.95 


. 3.12 


2.88 


8.87 




00,000 


1.44 


6.42 


8.04 


8.10 




800 


0.46 


0.80 


044 


0.18 




1,500 


0.48 


0.86 


0.48 


0.22 


50 


8,000 


0.52 


0.44 


0.56 


0.26 


15,000 


0.68 


0.96 


0.89 


0.77 




80,000 


0.62 


1 64 


1.31 


1.46 




00,000 


1.11 


2.89 


2.19 


3.26 




800 


0.40 


0.82 


0.44 


0.16 




1,500 


0.44 


84 


0.46 


0.20 


100 


8,000 


0.46 


38 


0.48 


0.22 


15,000 


0.52 


0.87 


0.78 


0.66 




80.000 


0.65 


1.46 


97 


0.97 




60,000 


1.01 


2.81 


1.68 


2.40 



From the foregoing tables (which are 
substantially as given by Beringer) it ap- 
pears that the hydraulic and pneumatic 
systems are not the cheapest in any of 
the cases considered; and the conclusion 



129 



seems to be that they are not suitable 
for long-distance transmission, except in 
cases where special circumstances pre- 
vent the use of either electricity or wire 
rope, or where the water or air may be 
of further use after being discharged. 
Thus the pneumatic method is specially 
adapted for use in tunnels, where it an- 
swers the double purpose of driving the 
machinery and ventilating the tunnel. 
On board war-ships, it has similar ad- 
vantages, with the further one that the 
fracture of a pipe during action will not, 
by the discharge of water or steam under 
pressure, produce injurious results on 
the men in the vicinity. 

Except in unusual cases, it would al- 
ways be more economical to place a local 
steam-engine if the power from it can be 
had at a cheaper rate than it can be 
brought from a distant source. If this 
source be water-power, then the local en- 
gine is more expensive in all the cases 
considered ; but if the source be a large 
steam-engine, the question of relative 
economy hinges on the distance and the 
amount of power. 



130 



In considering the foregoing tables, it 
must be noted that considerable reduc- 
tions in the price of dynamos and motors 
have been made since they were com- 
puted (1883) ; so that the showing should 
be somewhat more in favor of the elec- 
tric system than the tables give it. 

A careful study of the tables, bearing 
in mind the fact just stated, and the costs 
of producing the power in various sizes 
of engines previously given, leads to the 
following conclusions, within the limits 
of power and distances given in the 
table, the question of economy only being 
considered : 

It pays to transmit cheap water-power 
without regard to the amount of power 
or the distance ; and it pays to transmit 
cheap steam-power, provided the amount 
of energy required at any receiving sta- 
tion does not exceed about ten horse- 
power and the distance is not greater 
than about three miles. 

In all cases, wire-rope transmission is 
the cheapest for distances less than about 
three quarters of a mile ; beyond that 



rs. 



131 



distance, electric transmission is the 
cheapest. 

Of course, as suggested before, the 
question of convenience may be more im- 
portant than that of economy ; in which 
case the system of electric transmission, 
especially in the vicinity of the large gen- 
erating stations in our great cities, will 
usually be found preferable for even 
shorter distances than the limit above 
given. 



L- 



132 



HISTORICAL SKETCH. 

Thb first transmission was put up by 
the brothers Him in 1850, at a calico 
weaving establishment near Colmar. 
An immense mass of scattered build- 
ings seemed to forbid the possibility of 
using them and yet placing the motive 
power at any one point. In this emer- 
gency, they first tried this method of 
power transmission, using a riveted steel 
ribbon to each building from the engine- 
house. The steel bands were about 2^ 
inches wide by 0.04 inch thick, and 
ran on wood-faced drums. This pre- 
sented two inconveniences. In the first 
place, on account of its considerable sur- 
face, the band was liable to be agitated 
by the wind ; and secondly, it soon 
became worn and injured at the points 
where it was riveted. It served, however, 
very well for eighteen months to trans- 
mit twelve horse-power to a distance of 
250 feet. The success of the prin- 



133 



ciple was complete, bat much remained 
to be done before the wire rope and the 
rubber or leather-lined driving-wheel 
solved all difficulty and made this meth- 
od of transmitting power practically suc- 
cessful. 

The number of applications has in- 
creased very rapidly. At the end of 
1859, there were but few applications in 
use ; in 1862, there are known to have 
been about 400, and in 1867 about 800. 
At the present time there are thousands 
in successful operation. In 1864, a terri- 
ble explosion destroyed almost all of the 
great powder-mill at Ockhta, situated 
about &ix miles from St. Petersburg. 
The whole establishment was rebuilt. 
After studying many combinations, an 
artillery officer proposed to profit by the 
resources which this method offered to 
engineers, and thus to realize the only 
combination which could prove success^ 
ful in a powder-mill; namely, great dis- 
tance between the buildings, so that the 
explosion of one should not entail the 
ruin of the rest. The new establishment, 
which went into operation in 1867, is com- 



134 

posed of thirty-four different workshops 
or laboratories, to which motive power is 
transmitted by means of wire ropes 
driven by three turbines, thus distrib- 
uting a total of 274 horse-power along a 
line nearly a mile in length. 

One of the largest transmissions is that 
employed to utilize the falls of the 
Rhine near Schaff hausen, in Switzerland. 
Advantage was taken of the rapids atone 
side, to put in a number of turbines, 
but since the steep, rocky banks forbade 
the erection of any factories in the imme- 
diate vicinity, the entire power was 
transferred diagonally across the stream 
to the town, more than half a mile 
farther down, and there distributed, cer- 
tain rocks in the water being made use 
of to set up the required intermediate 
stations. 

There are three turbines giving out 
collectively about 700 horse-power. There 
are two wheels fifteen feet in diameter, 
keyed on a horizontal shaft running 
over the three turbines and geared 
with them all. Two wire ropes, f inch 
in diameter, run right across the river. 



135 



a distance of 370 feet. Here two sec- 
ondary wheels are fitted, which drive 
two secondary ropes running up the 
banks of the river for a distance of 1500 
feet, this distance being subdivided into 
three lengths. From the end station 
about 400 horse- power are transmitted 
to a farther distance of 1500 feet ; so 
that the total length of rope transmission 
amounts to 3370 feet 

Another very large and interesting 
transmission was erected in 1872 at Belle- 
garde,* a small town near the confluence 
of the Rhone and a mountain torrent 
called the Valserine, about fifteen miles 
from Geneva. The total disposable 
horse-power is estimated at 12000, of 
which only about one fourth has been 
utilized. This power is obtained by 
means of six Jonval turbines, each of 630 
horse-power ; and it is transmitted from 
each turbine by a pair of ropes running 
side by side, so connected by differential 
gear as to close the sluice of the turbine 
in case a rope should break. 



See " Engineer," vol. 37, 1874. 



136 



The wheels are 18 feet in diameter, and 
make 70 revolutions per minute, giving 
the rope a velocity of 3920 feet. The 
ropes are 1^ inch in diameter. The power 
from the different turbines is transmitted 
in different directions. 

Among other industries at Bellegarde 
thus supplied with power, an interesting 
case is that of a phosphate-mill, which 
receives about 300 horse-power by means 
of a pair of ropes. The turbines are 
down in a ravine, so that each rope first 
run upwards at a steep inclination over 
a pair of carrying-sheaves (Plate I), whose 
vertical and horizontal distances from 
the lower wheel are 116 and 197 feet re- 
spectively; and then round a wheel at the 
first intermediate station (Plate II) at a 
further distance of 430 feet. Then fol- 
low other stations at distances of 426, 
426, 571, 290, and 634 feet, making a to- 
tal of 2974 feet. 

The object of running the inclined 
rope over the carrying-sheaves and 
through to the second station is to give 
th^ inclined portions the requisite ten- 
sion, as previously explained. 



137 

Examples might be multiplied, but 
the above are sufficient to illustrate the 
extent of the practical applications of this 
method of transmitting power, which 
by its low cost of erection and mainten- 
ance, and its high efficiency, has dem- 
onstrated its undoubted superiority, from 
an economic standpoint, over all other 
systems of transmitting power, for dis- 
tances ranging from 100 to 3500 feet.